King penguins (Aptenodytes patagonicus) undergo an annual catastrophic moult during which they replace their entire collection of feathers all at once. For a period of a month or so, they are unable to swim (they are no longer waterproof, apparently) so they stay on land and just wait for the process to complete. Here’s a penguin from Gold Harbour in South Georgia in the middle of its moult. All the sites we visited on the island were covered in a thin layer of penguin feathers.
For the technically inclined...